<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>tangent</title>
  </head>
  <body bgcolor="#FFFFFF">
    <center>Scilab Function</center>
    <div align="right">Last update : 31/10/2006</div>
    <p>
      <b>tangent</b> -  linearization of a dynamical system at an equilibrium point</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[f,g,newm]=tangent(ff,xe,[ue])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>ff</b>
        </tt>: a string which gives the name of the Scilab function which  codes
	    the system, or the fuunction itself.</li>
      <li>
        <tt>
          <b>xe</b>
        </tt>: column vector which gives the equilibrium point for the value ue of the parameter</li>
      <li>
        <tt>
          <b>ue</b>
        </tt>: real value.</li>
      <li>
        <tt>
          <b>f, g</b>
        </tt>: two matrices for the linearised  system  <tt>
          <b>dxdot=f.dx + g.du</b>
        </tt>
      </li>
      <li>
        <tt>
          <b>newm</b>
        </tt>: A new macro of type [y]=newm(t,x,u) which computes the field of the linearised system  (newm(t,xe,ue)=0)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    linearises around the equilibrium point <tt>
        <b>(xe,ue)</b>
      </tt> the vector field of 
    the dynamical system given by a Scilab macro <tt>
        <b>ff</b>
      </tt>, <tt>
        <b>xdot=ff(t,x,[u])</b>
      </tt>.
    The dynamical system is supposed to be autonomous.</p>
  </body>
</html>
